Pakati pesimba rinokwevera pasi, kana kuti pakati pesimba, ipfungwa huru mufizikisi neinjiniya inoshandiswa kuona kuenzana uye kugadzikana kwechinhu. Pakati pesimba rinokwevera pasi ndiyo nzvimbo iyo simba resimba rinokwevera pasi rinoonekwa serinonyanya kusimba uye apo simba rinokwevera pasi rinofungidzirwa kuti rinoshanda. Kunzwisisa pfungwa iyi kwakakosha mukushandiswa kwakasiyana-siyana, kubva pakugadzira chivakwa kusvika pakuongorora kufamba kwechinhu. Chinyorwa chino chichakurukura tsananguro yepakati pesimba rinokwevera pasi, maitiro ekuverenga pakati pesimba rinokwevera pasi kune maumbirwo akasiyana-siyana echinhu, uye mimwe mienzaniso yezvinetso kuti kujekeswe pfungwa iyi.
Tsanangudzo yeCenter of Gravity
Pakati pesimba rinokwevera pasi (pakati pesimba) ndiyo nzvimbo iri muchinhu apo huremu hwese hwechinhu hunogona kutariswa hwakanangana nechinangwa chekuverenga masimba nenguva. MuCartesian coordinate system, pakati pesimba rinokwevera pasi rechinhu chine huremu hwakagoverwa hunogona kuverengerwa uchishandisa fomura inotevera:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i}
\]
\[
z_{\text{cm}} = \frac{\sum (z_i \cdot m_i)}{\sum m_i}
\]
Apo \( (x_i, y_i, z_i) \) pane ma coordinates echinhu chikuru \( m_i \).
Nzvimbo Yekukwevera Zvinhu Pasi Pemaumbirwo Akasiyana-siyana
1. Nzvimbo Yekukwevera Zvinhu Zvakafanana
Kune zvinhu zvakafanana (zvine huwandu hwakafanana), pakati pegiravhiti (gravity) panogona kuonekwa nenzira iri nyore. Semuenzaniso:
– Tsvimbo Tsvimbo Tsvimbo: Pakati pesimba regiravhiti retsvimbo yakatetepa, yakafanana ine urefu \( L \) iri pakati petsvimbo, kureva \( x = \frac{L}{2} \).
– Chinyorwa cheRectangular: Pakati pegiravhiti yeslab ine rectangular yakafanana ine urefu \( L \) nehupamhi \( W \) iri panzvimbo inoungana diagonals, kureva pa \( x = \frac{L}{2} \) uye \( y = \frac{W}{2} \).
– Plate yeTriangular: Pakati pegiravhiti yeplate yetriangular yakafanana iri pachikamu chimwe muzvitatu chepakati petriangular imwe neimwe. Kune triangle ine vertex coordinates \( A(x_1, y_1) \), \( B(x_2, y_2) \), uye \( C(x_3, y_3) \):
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3}
\]
2. Nzvimbo Yekukwevera Zvinhu Zvisingaenzane
Kune zvinhu zvisina kufanana (zvine huwandu husina kufanana), pakati pesimba regiravhiti panofanira kuverengerwa nekukamura chinhu kuita zvinhu zvidiki uye kuverenga pakati pazvo pesimba regiravhiti uchishandisa fomura integral. Semuenzaniso, kune chinhu chine huwandu hwakasiyana \( \rho(x, y, z) \):
\[
x_{\text{cm}} = \frac{\int x \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
y_{\text{cm}} = \frac{\int y \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
\[
z_{\text{cm}} = \frac{\int z \cdot \rho(x, y, z) \, dV}{\int \rho(x, y, z) \, dV}
\]
Muenzaniso weCenter of Gravity Mibvunzo
Muenzaniso Mubvunzo 1: Pakati pesimba retsvimbo yakatetepa
Mubvunzo:
Verenga pakati pesimba rinokwevera pasi retsvimbo yakatetepa, yakafanana ine urefu hwemamita gumi.
Mhinduro:
Sezvo tsvimbo yacho yakafanana, pakati pesimba rinokwevera pasi riri pakati petsvimbo:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{10 \, \text{m}}{2} = 5 \, \text{m}
\]
Saka, pakati pesimba rinokwevera pasi retsvimbo yakatetepa iri mamita mashanu kubva kumugumo mumwe wetsvimbo.
Muenzaniso Mubvunzo 2: Pakati pesimba regiravhiti reRectangular Plate
Mubvunzo:
Verenga pakati pegiravhiti resimbi ine rectangular yakafanana ine urefu hwemamita masere uye upamhi hwemamita mana.
Mhinduro:
Pakati pegiravhiti yeplate ine rectangular yakafanana iri pamharadzano ye diagonals, dzinoti:
\[
x_{\text{cm}} = \frac{L}{2} = \frac{8 \, \text{m}}{2} = 4 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{W}{2} = \frac{4 \, \text{m}}{2} = 2 \, \text{m}
\]
Saka, pakati pegiravhiti yeplate rectangular (4 m, 2 m).
Muenzaniso Mubvunzo 3: Pakati peGravity yeTable Triangular
Mubvunzo:
Verenga pakati pegiravhiti yeplate ine mativi matatu yakafanana ine vertices pa coordinates \( A(0, 0) \), \( B(6, 0) \), uye \( C(3, 6) \).
Mhinduro:
Pakati pegiravhiti yeplate ine mativi matatu yakafanana inogona kuverengerwa uchishandisa fomura:
\[
x_{\text{cm}} = \frac{x_1 + x_2 + x_3}{3} = \frac{0 + 6 + 3}{3} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{y_1 + y_2 + y_3}{3} = \frac{0 + 0 + 6}{3} = \frac{6}{3} = 2 \, \text{m}
\]
Saka, pakati pegiravhiti yeplate ine mativi matatu (3 m, 2 m).
Muenzaniso Mubvunzo 4: Pakati peSisitimu yeKukweva Simba reChidimbu
Mubvunzo:
Sisitimu ine zvidimbu zvitatu zvine huremu hwakafanana hwe2 kg chimwe nechimwe, zviri panzvimbo dzinoenderana \( (1, 2) \), \( (3, 4) \), uye \( (5, 6) \). Verenga pakati pegiravhiti yesystem yezvikamu.
Mhinduro:
Sezvo huwandu hwezvikamu zvacho hwakafanana, tinogona kushandisa fomura iri nyore kuverenga pakati pegiravhiti:
\[
x_{\text{cm}} = \frac{\sum (x_i \cdot m_i)}{\sum m_i} = \frac{(1 + 3 + 5) \cdot 2}{3 \cdot 2} = \frac{9}{3} = 3 \, \text{m}
\]
\[
y_{\text{cm}} = \frac{\sum (y_i \cdot m_i)}{\sum m_i} = \frac{(2 + 4 + 6) \cdot 2}{3 \cdot 2} = \frac{12}{3} = 4 \, \text{m}
\]
Saka, pakati pegiravhiti yesystem yezvikamu ndeye (3 m, 4 m).
Mhedziso
Pakati pesimba rinokwevera pasi ipfungwa inokosha mufizikisi neinjiniya. Kunzwisisa maverengero epakati pesimba rinokwevera pasi kune maumbirwo akasiyana-siyana ezvinhu uye masisitimu ezvimedu kwakakosha pakuongorora kuenzana nekugadzikana. Chinyorwa chino chakurukura tsananguro yepakati pesimba rinokwevera pasi, maverengero epakati pesimba rinokwevera pasi kune zvinhu zvakafanana uye zvisina kufanana, uye chapa mienzaniso yakati wandei yezvinetso kuti zvibatsire kujekesa pfungwa iyi.
Muhupenyu hwezuva nezuva, kunzwisisa nzvimbo yesimba rinokwevera pasi kunobatsira zvikuru mumabasa akasiyana-siyana, kubva pakugadzira chivako kusvika pakugadzira tekinoroji. Nekunzwisisa nekushandisa pfungwa yenzvimbo yesimba rinokwevera pasi, tinogona kugadzira zvivakwa zvakagadzikana uye zvakachengeteka uye kunzwisisa zviri nani mafambiro ekufamba kwechinhu.
